Knowledge Organiser: Conditional Probability
Part of Conditional Probability · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Conditional Probability within Conditional Probability for GCSE Mathematics. Revise Conditional Probability in Probability for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 5 of 5 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 5 of 5
Practice
14 questions
Recall
12 flashcards
Knowledge Organiser: Conditional Probability
Key Terms
- Conditional probability: The probability of A given that B has already occurred
- P(A|B): Read as "probability of A given B"
- P(A ∩ B): The probability that both A and B occur
- Reduced sample space: Restricting outcomes to only those where condition B is true
- Given condition: The event after the | symbol that is known to have happened
Must-Know Facts
- P(A|B) is read "probability of A given B"
- The condition (B) becomes your new sample space — only consider outcomes where B is true
- P(B) must be greater than 0 for the formula to work
- Conditional probability is used on the second branch of a tree diagram
- In two-way tables: use the row/column total as the denominator
- The result is still a probability — must be between 0 and 1
Key Formulas
- P(A|B) = P(A ∩ B) ÷ P(B)
- P(A ∩ B) = P(B) × P(A|B)
- From a table: P(A|B) = (count of A and B) ÷ (total count of B)
Common Mistakes
- Wrong denominator: P(A|B) is conditional on B — divide by P(B), not the total probability
- Confusing P(A|B) with P(B|A): These are different — order matters in conditional probability
- From a two-way table: The denominator is the row or column total for the given condition, not the grand total
- Independent events check: If P(A|B) = P(A), the events are independent — use this to verify
Revise this topic interactively on PrepWise — self-test mode, tap-to-reveal definitions, and Common Mistakes from examiners.
Try the interactive Knowledge Organiser — free →Keep building this topic
Read this section alongside the surrounding pages in Conditional Probability. That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Conditional Probability
What does the notation P(A|B) mean?
P(A) = 0.4, P(B) = 0.3 and P(A ∩ B) = 0.12. Using conditional probability, determine whether A and B are independent events. You must show all your working and give a reason for your conclusion.
Quick Recall Flashcards
14 questions on Conditional Probability — practise free
Instant marking, adaptive difficulty, and 12 spaced repetition flashcards. Free until your GCSEs.
Try PrepWise Free